A Novel Approach to Find Pseudo–peripheral Vertices for Snay’s Heuristic

Sanderson Gonzaga de Oliveira, Júnior A. B. Bernardes

Abstract

The solution of linear systems represented by Ax = b is fundamental in many numerical simulations in science and engineering. Reducing the profile of A can reduce the storage requirements and time processing costs of solving such linear systems. In this work, we propose a generalized algorithm for finding pseudo–peripheral vertices for Snay’s heuristic. In experiment performed on 36 instances contained in the Harwell-Boeing and SuiteSparse matrix collections, it has been found that the number of pseudo– peripheral vertices selected in Snay’s heuristic may be suitable for small instances, but it is insufficient to obtain reasonable results in instances that are not small. This paper recommends to select up to 26% (0.3%) of pseudo–peripheral vertices in relation to the instance size when applied to instances smaller than 3,000 (larger than 20,000) vertices.